How do you create a rounded, inset beveled edge?
Similiar to creating the control edge loops manually (as stated in stauVictors answer), you can create them procedurally with the bevel modifier. Using a bevel modifier before a Subdivision Surface modifier, is common practice to prevent smoothing on sharp edges.

Create a vertex group for the edges, which are supposed to stay sharp and assign the edges to it

Then add a bevel modifier and select that group as the Vertex Group of the modifier. If you use more segments in the Bevel modifier, the following subdivision modifier will have less effect on the beveled segments.



Edit from Coffeehouse's comment: As an alternative to the Vertex Group, you can choose weight as the Limit Method and create Bevel Weights for the mesh.